Forecast Combination Research Articles

Formalizing a Postprocessing Procedure for Linear–Convex Combination Forecasts

ABSTRACTWe investigate mean squared forecast error (MSE) accuracy improvements for linear–convex combination forecasts, whose components are pretreated by a postprocessing procedure called “vector autoregressive forecast error modeling” (VAFEM). Assuming that the forecast error series of the individual forecasts are governed by a stable VAR process under classic conditions, we obtain the following results: (i) VAFEM treatment bias corrects all individual and linear–convex combination forecasts. (ii) Any VAFEM‐treated combination has a smaller theoretical MSE than its untreated analog, if the VAR parameters are known. (iii) In empirical applications, VAFEM gains depend on (1) in‐sample sizes, (2) out‐of‐sample forecast horizons, and (3) the biasedness of the untreated forecast combination. We demonstrate the VAFEM capacity in simulations and for realized‐volatility forecasting, using S&P 500 data.

PHOTOVOLTAIC GENERATION FORECASTING MODELS: CONCEPTUAL ENSEMBLE ARCHITECTURES

The decisions regarding power regulation, energy resource planning, and integrating “green” energy into the electrical grid hinge on precise probabilistic forecasts. One of the potential strategies to enhance forecast accuracy is the utilization of ensemble forecasting methods. They represent an approach where multiple models collaborate to achieve superior results compared to what a single model could produce independently. These methods can be categorized into two main categories: competitive and collaborative ensembles. Competitive ensembles harness the diversity of parameters and data to create a rich pool of base models. This approach may encompass statistical analysis, noise filtering, and anomaly elimination. On the other hand, collaborative ensembles rely on the interaction among models to achieve better outcomes. These methods encompass strategies such as weighted predictions, voting, aggregation, and a combination of model results. The research of ensemble forecasting methods in the context of photovoltaic generation is highly relevant, as solar energy represents a crucial source of renewable energy. Accurate predictions of solar energy production address the challenges related to the efficient utilization of photovoltaic panels and their integration into the overall energy system. This paper investigates conceptual ensemble architectures for photovoltaic energy forecasting. These architectures encompass various methods of aggregating base models within an ensemble, allowing for the consideration of different aspects and peculiarities of solar data, such as solar irradiation intensity, meteorological conditions, geographic factors, and more. These conceptual models are developed based on well-established statistical, machine learning, and artificial intelligence methods. Therefore, this paper provides an overview of ensemble forecasting methods for renewable energy, covering competitive and collaborative ensembles, as well as developing conceptual models for solar energy forecasting. This work aims to elevate the accuracy and efficiency of forecasts in the realm of renewable energy, representing a significant step in the advancement of sustainable and environmentally friendly energy production. Keywords: probabilistic solar forecasting, ensemble model, forecast combination, competitive ensembles, collaborative ensembles, conceptual models.

Combining Volatility Forecasts of Duration‐Dependent Markov‐Switching Models

ABSTRACTDuration‐dependent Markov‐switching (DDMS) models require a user‐specified duration hyperparameter, for which there is currently no established procedure for estimation or testing. As a result, an ad‐hoc duration choice must be heuristically justified. This paper proposes a methodology for handling duration selection in DDMS models, with a focus on volatility forecasting. The main novelty lies in generating forecasts through model combination techniques. The idea is that the combined forecasts will be more robust to misspecification in selecting the duration structure, thus yielding more accurate forecasts. Additionally, the paper contributes to the literature by evaluating the out‐of‐sample volatility forecasting performance of DDMS models compared to benchmark conditional volatility models. Empirical analysis involves returns from three distinct asset classes: a cryptocurrency, a stock market index, and a foreign currency exchange rate. Various volatility proxies and robust loss functions are incorporated into our analysis. The results indicate that combined forecasts outperform individual models and, in some cases, are more accurate than GARCH and MS‐GARCH models. Furthermore, models with fixed duration typically underperform relative to the simple GARCH model, often resulting in test rejections.

Forecasting economic growth by combining local linear and standard approaches

Today, developing economies are of major importance for global macroeconomic development. However, the empirical analysis and especially the forecasting of macroeconomic time series remain difficult due to a lack of sufficient data, data frequency, high volatility, and non-linear developments. These difficulties require more sophisticated approaches to obtain reliable forecasts. Therefore, we propose an improved forecasting method especially for growth data based on a data-driven local linear trend estimation with an extended iterative plug-in algorithm for determining the bandwidth endogenously. This approach allows a smooth trend estimation that takes care of temporary changes in trend processes. Further, the naïve random walk model is extended for forecasting by including a local linear, time-varying drift. We apply this method to GDP development for six developing and two advanced economies and compare different forecast combinations. The combinations that include the local linear approach and the random walk with a local linear trend improve forecasting accuracy and reduce variance.

Forecasting exchange rate volatility: An amalgamation approach

The importance of exchange rate volatility forecasting has both practical and academic merit. Our aim is to provide a comprehensive analysis of the forecasting ability of financial and macroeconomics variables for future exchange rate volatility. We employ seven widely traded currencies against the US dollar and examine linear models and a variety of machine learning, dimensionality reduction and forecast combination approaches, along with creating a grand forecast (amalgamation approach) from these approaches. Our findings highlight the predictive power of the amalgamation approach, as well as the positive contribution of macroeconomic and financial variables in the forecasting experiment. Furthermore, we generate forecasts on the separate frequencies of volatility using wavelet analysis, in order to extract frequency-related information and examine timing effects in the performance of the methods.

An energy management method for combined load forecasting of fuel cell ships

Abstract The article proposes an energy management method (EMM) for fuel cell ships, which consists of two parts: load forecasting (LF) and real-time optimized scheduling (RTOS). LF is composed of Long Short-Term Memory neural networks, which are capable of being trained to predict future loads based on historical ship load information. RTOS consists of model predictive control and can allocate energy in real time. Initially, shiploads and battery status are collected in real time, and then LF passes the predicted load sequence to RTOS. RTOS optimizes real-time energy allocation based on the predicted load and the current operating status of two sets of batteries, while meeting system constraints and maintaining the battery SOC at a healthy level, to minimize operational cost consumption. The simulations demonstrate that the EMM can consistently maintain SOC at a healthy level and reduce fuel cell ship operating costs to some extent, thereby improving economic efficiency.

Decision-focused linear pooling for probabilistic forecast combination

In real-world settings, decision-makers often have access to multiple forecasts for the same unknown quantity. Combining different forecasts has long been known to improve forecast quality, as measured by scoring rules in the case of probabilistic forecasting. However, improved forecast quality does not always translate into better decisions in a downstream problem that utilizes the resultant combined forecast as input. To this end, this work proposes a novel probabilistic forecast combination approach that accounts for the downstream stochastic optimization problem by which the decisions will be made. We propose a linear pool of probabilistic forecasts where the respective weights are learned by minimizing the expected decision cost of the induced combination, which we formulate as a nested optimization problem. Two methods are proposed for its solution: a gradient-based method that utilizes differential optimization layers, and a performance-based weighting method. The proposed decision-focused combination approach is validated in two integral problems associated with renewable energy integration in low-carbon power systems and compared against well-established combination methods. Namely, we examine an electricity market trading problem under stochastic solar production and a grid scheduling problem under stochastic wind production. The results illustrate that the proposed approach leads to lower expected downstream costs, while optimizing for forecast quality when estimating linear pool weights does not always translate into better decisions. Notably, optimizing for a combination of downstream cost and an accuracy-oriented scoring rule consistently leads to better decisions while also improving forecast quality.

Variable‐weight combined forecasting model with causal analysis and clustering for refined oil sales forecasting

AbstractForecasting refined oil sales is essential in energy supply chain management. However, accurate forecasting is limited by several factors, including multiple influences of external features, heterogeneity of different gasoline stations, and difficulty in balancing linear and nonlinear forecasting. To address these issues, we propose a novel variable‐weight combined forecasting model. In the first stage, the model incorporates causal analysis and clustering methods to provide a quantitative description of multiple effects of external features and highly correlated aggregation of homogeneous data. Subsequently, based on the patterns of external feature influences learned from historical data, variable‐weight combined forecasting is realized to balance linear and nonlinear forecasting dynamically. Experiments based on real sales data procured from several regions demonstrate that the proposed model outperforms other benchmark and widely used models in terms of forecasting accuracy and statistical significance. The ablation experimental results confirm the significance of causal analysis, clustering, and variable‐weight combined forecasting in improving the balance between linear and nonlinear forecasting. Moreover, our results indicate that improving the quality of clustering can yield greater benefits than improving the amount of training data. Finally, we also explore whether the forecasting superiority translates into better inventory control, and our results show that the proposed optimization model can effectively balance inventory cost and service level, while also better suppress the bullwhip effect.

Enhancing Agricultural Commodity Forecasting: A Median-Based Combination of Time Series Models

This study explores the efficacy of combining forecasts using the median operator to enhance forecasting performance. The traditional approach of assigning equal weights to individual models often struggles with extreme forecasts. A new method Simple Combination of Univariate Models (SCUM) is utilized, which uses the median operator to combine forecasts from four distinct time series models: Exponential Smoothing (ETS), Auto Regressive Integrated Moving Average (ARIMA), Dynamically Optimised Theta Model (DOTM), and Complex Exponential Smoothing (CES). This approach aims to mitigate the influence of extreme forecasts and improve overall accuracy. Our empirical analysis investigates the use of the SCUM approach for the agricultural commodity data. Yearly production of Rice is used, sourced from the Ministry of Agriculture & Farmers Welfare, Government of India. The forecasting performance of the SCUM approach is compared against individual models and a mean-based combined forecast using key performance metrics such as Mean Absolute Percentage Error (MAPE), Root Mean Squared Error (RMSE), and Relative Efficiency. The results show that SCUM outperforms all other models, achieving the lowest RMSE (51.89) and a MAPE of 6.90, indicating superior in-sample forecasting accuracy. ARIMA was the least efficient with a 22.11% relative efficiency, while the Mean combination method (3.33%) was closest to SCUM in performance. The findings suggest that SCUM is not only a viable alternative to traditional methods but also offers significant advantages in improving forecasting accuracy. This research underscores the potential for median-based forecast combinations to achieve superior predictive accuracy and reliability, making it a valuable tool for scholars and practitioners in time series forecasting.

Evaluating Wind Speed Forecasting Models: A Comparative Study of CNN, DAN2, Random Forest and XGBOOST in Diverse South African Weather Conditions

The main source of electricity worldwide stems from fossil fuels, contributing to air pollution, global warming, and associated adverse effects. This study explores wind energy as a potential alternative. Nevertheless, the variable nature of wind introduces uncertainty in its reliability. Thus, it is necessary to identify an appropriate machine learning model capable of reliably forecasting wind speed under various environmental conditions. This research compares the effectiveness of Dynamic Architecture for Artificial Neural Networks (DAN2), convolutional neural networks (CNN), random forest and XGBOOST in predicting wind speed across three locations in South Africa, characterised by different weather patterns. The forecasts from the four models were then combined using quantile regression averaging models, generalised additive quantile regression (GAQR) and quantile regression neural networks (QRNN). Empirical results show that CNN outperforms DAN2 in accurately forecasting wind speed under different weather conditions. This superiority is likely due to the inherent architectural attributes of CNNs, including feature extraction capabilities, spatial hierarchy learning, and resilience to spatial variability. The results from the combined forecasts were comparable with those from the QRNN, which was slightly better than those from the GAQR model. However, the combined forecasts were more accurate than the individual models. These results could be useful to decision-makers in the energy sector.

Shapley‐value‐based forecast combination

AbstractThis paper puts forward a new and simple method to combine forecasts, which is particularly useful when the forecasts are strongly correlated. It is based on the Mincer Zarnowitz regression, and a subsequent determination using Shapley values of the weights of the forecasts in a new combination. For a stylized case, it is proved that such a Shapley‐value‐based combination improves upon an equal‐weight combination. Simulation experiments and a detailed illustration show the merits of the Shapley‐value‐based forecast combination.

Incorporating judgment in forecasting models in times of crisis

AbstractThis paper introduces a simple and reproducible method to modify model forecasts using expert forecasts which is useful in crisis times. The idea is to add the expert forecast as an additional observation of the dependent variable, and to extend the model with an additional explanatory variable such as the square of a deterministic trend. Next, the new model forecast is combined with the expert forecast using equal weights. We show that it works well for gross domestic product growth forecasts for 2020 for 12 countries and that it improves upon an equal‐weighted combination of the original model forecast and expert forecast.

Forecasting crude oil volatility and stock volatility: New evidence from the quantile autoregressive model

This paper employs the quantile autoregressive (QAR) model to examine the forecasting relationship between stock volatility and crude oil volatility. We first utilize the sup-Wald test to evaluate Granger causality across various quantile levels, providing valuable information for forecasting. Our findings reveal that the causal effects between stock volatility and crude oil volatility differ considerably across different quantiles, with a V-shaped relationship evident at the quantile level. Results from out-of-sample forecasts indicate that the forecasting effect of oil volatility on stock volatility has both positive and negative impacts. In contrast, when using stock volatility to forecast crude oil volatility, predictability improves relative to the benchmark, particularly at more extreme quantiles. Further analysis highlights the necessity of forecast combinations to achieve an overall improvement in forecasting tasks.

Enhancing Urban Flood Forecasting: Integrating Weather Forecasts and Hydrological Models

Precipitation data in urban hydrological models are derived from an ideal stormwater model, which has some uncertainties and limited prediction times. Therefore, to reliably forecast urban flooding, prolong prediction time periods, and better support associated research in urban flood forecasting, a combination of weather forecasts and urban hydrology is necessary. By applying comprehensive cloud microphysical schemes in the Weather Research and Forecasting (WRF) model to the predecessor torrential rainfall associated with Typhoon Khanun (2017), this study evaluated different configurations of atmospheric-hydrological simulations based on the WRF model and InfoWorks ICM. Results showed that the microphysics scheme could significantly affect spatial and temporal distributions of the simulated torrential rainfall. Generally, the combination of WRF and NSSL schemes produced better performance. Applying the NSSL scheme to the WRF model and combining it with the InfoWorks ICM system can reproduce torrential rainfall and urban flood formations.

A Wind Power Combination Forecasting Method Based on GASF Image Representation and UniFormer

In the field of wind power prediction, traditional methods typically rely on one-dimensional time-series data for feature extraction and prediction. In this study, we propose an innovative short-term wind power forecasting approach using a “visual” 2D image prediction method that effectively utilizes spatial pattern information in time-series data by combining wind power series and related environmental features into a 2D GASF image. Firstly, the wind power data are decomposed using the ICEEMDAN algorithm optimized by the BWO (Beluga Whale Optimization) algorithm, extracting the submodal IMF (Intrinsic Mode Function) components with different frequencies. Then, modal reconstruction is performed on the basis of the permutation entropy value of the IMF components, selecting meteorological features highly correlated with reconstructed components through Spearman correlation analysis for data splicing and superposition before converting them into GASF images. Finally, the GASF images are input into the UniFormer model for wind power sequence prediction. By leveraging wind power data predictions from a coastal wind farm in East China and Sotavento in Spain, this study demonstrates the significant benefits and potential applications of this methodology for precise wind power forecasting. This research combines the advantages of image feature extraction and time-series prediction to offer novel perspectives and tools for predicting renewable energy sources such as wind power.

A Transcendental LASSO Function for Combining Machine Learning and Statistical Model Forecasts

The aim of the study is the development of methodology for accurate estimation of electric vehicle demand; which is paramount regarding various aspects of the firms decision-making such as optimal price, production level, and corresponding amounts of capital and labor; as well as supply chain, inventory control, capital financing, and operational expenses management. The forecasting methods utilized include statistical techniques (autoregressive integrated moving average [ARIMA], and polynomial regression), machine learning (nonlinear autoregressive neural network [NAR]), deep learning (long short-term memory [LSTM]), hybrid and combination forecasting. With regard to the latter method, our study experiments with four different combining model approaches, including the introduction of an original, novel combining method with the employment of a transcendental LASSO function, which is used to form combinations of forecasts generated by the NAR, ARIMA, and polynomial regression models. The LASSO-based combining model proved superior to all other models, for the majority of forecast error statistics; where the root mean square error (RMSE) and mean absolute percentage error (MAPE) values are 4.5% and 8% respectively lower than the average level of the component model forecasts. The major implications of our empirical findings are that greater accuracy in demand forecasting can be achieved with a combining model approach, rather than reliance on any particular, singular model. Furthermore, given its superior performance, the employment of the studys LASSO-based combining model to forecast electric vehicle demand may lead to optimal firm decision-making over a range of organizational facets, which is predicated on accurate demand function estimation.

Portfolio Optimization with Sector Return Prediction Models

We analyze return predictability for U.S. sectors based on fundamental, macroeconomic, and technical indicators and analyze whether return predictions improve tactical asset allocation decisions. We study the out-of-sample predictive power of individual variables for forecasting sector returns and analyze multivariate predictive regression models, including OLS, regularized regressions, principal component regressions, the three-pass regression filter, and forecast combinations. Using an out-of-sample Black–Litterman portfolio optimization framework and employing predicted returns as investors’ ‘views’, we evaluate the benefits of sector return forecasts for investors. We find that portfolio optimization with sector return prediction models significantly outperforms portfolios using historical averages as well as passive benchmark portfolios.

Forecast combination with multivariate grey prediction for tourism demand forecasting

Empirical evidence has shown that forecast combination can improve the prediction accuracy of tourism demand forecasting. This paper aimed to develop a more accurate grey forecast combination method (GFCM) with multivariate grey prediction models In light of the practical applicability of grey prediction, which is not required to apply any statistical test to examine data series this research features the use of multivariate grey models through the genetic algorithm to synthesize forecasts from univariate grey prediction models commonly used in tourism forecasting into composite forecasts Empirical results showed that the proposed GFCM significantly outperformed the other combination methods considered. The results also suggested that the risk of forecast failures caused by selecting an inappropriate single model for tourism demand forecasting can be reduced by using the GFCM.

Measuring persistent global economic factors with output, commodity price, and commodity currency data

AbstractIn this study, we use monthly G7 industrial production data, commodity price index data, and commodity currency exchange rate data in a dynamic factor model to examine the global economic factors useful for commodity price prediction. We differentiate between the dynamic factors by specifying a persistent factor and a non‐persistent factor, both as a single global factor using all data and as factors for each category of data. The in‐sample predictive performances of the three persistent factors together are better than the non‐persistent factors and the single global factors. Out‐of‐sample outcomes based on forecast combinations also support the presence of predictive information in the persistent factors for overall commodity prices and for most sub‐categories of commodity price indexes relative to their means. The gains in forecast accuracy are heterogeneous, ranging from 5% to 7% in the 1‐ to 6‐month horizon for overall commodity prices to a high of around 20% for fertilizers in the 12‐month horizon in the recent sample. We further show that the information in the persistent factors, especially in the commodity currency exchange rate‐based persistent factor, can be integrated with other global measures to further improve the predictive performances of the global measures.

Assimilation of PSO and SVR into an improved ARIMA model for monthly precipitation forecasting

Precipitation due to its complex nature requires a comprehensive model for forecasting purposes and the efficiency of improved ARIMA (IARIMA) forecasts has been proved relative to the conventional models. This study used two procedures in the structure of IARIMA to obtain accurate monthly precipitation forecasts in four stations located in northern Iran; Bandar Anzali, Rasht, Ramsar, and Babolsar. The first procedure applied support vector regression (SVR) for modeling the statistical characteristics and monthly precipitation of each class, IARIMA-SVR, which improved the evaluation metrics so that the decrease of Theil's coefficient and average relative variance in all stations was 21.14% and 17.06%, respectively. Two approaches are defined in the second procedure which includes a forecast combination (C) scheme, IARIMA-C-particle swarm optimization (PSO), and artificial intelligence technique. Generally, most of the time, IARIMA-C-PSO relative to the other approach, exhibited acceptable results and the accuracy improvement was greater than zero at all stations. Comparing the two procedures, it is found that the capability of IARIMA-C-PSO is higher concerning the IARIMA-SVR, so the decrease in the normalized mean squared error value from IARIMA to IARIMA-SVR and IARIMA-C-PSO is 36.72% and 39.92%, respectively for all stations. The residual predictive deviation (RPD) of IARIMA-C-PSO for all stations is greater than 2, which indicates the high performance of the model. With a comprehensive investigation, the performance of Bandar Anzali station is better than the other stations. By developing an improved ARIMA model, one can achieve a high performance in structure identifying and forecasting of monthly time series which is one of the issues of interest and importance.